failed because my internal domain (on a LAN) was used as the identifying mail address, as machinename.LAN

I'm a bit confused by reading the man pages for hostname, setdomainname, myname, and so on, but I need to preserve DNS / DHCP for my machine, since behind a router.

Ah, networking...

I *think* this will solve it:

All you have to do is to edit as root the file /etc/hosts and include a fictitious FQDN for your machine. For example, the machine GX300 with IP number 192.168.0.7, could have as the fictitious FQDN GX300.test.net, and be entered in the HOSTS file as follows: